As shown in Fig. REF , we use a bi-directional forward-backward diffeomorphic registration network to estimate the INF motion field \(\phi \) . Our network is modeled as a generative stochastic variational autoencoder (VAE) [1]}. Let \(x\)  and \(y\)  be a 2D image pair, and let \(z\)  be a latent variable that parameterizes the INF motion field \(\phi : \mathbb {R}^{2}\rightarrow \mathbb {R}^{2}\) . Following the methodology of a VAE, we assume that the prior \(p(z)\)  is a multivariate Gaussian distribution with zero mean and covariance \(\Sigma _{z}\) :
\(p(z)\sim \mathcal {N}(z;0,\Sigma  _{z}) .\) 
